Atkin-Lehner |
3+ 11+ 13+ 19- |
Signs for the Atkin-Lehner involutions |
Class |
89661a |
Isogeny class |
Conductor |
89661 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
138240 |
Modular degree for the optimal curve |
Δ |
778667858397 = 38 · 113 · 13 · 193 |
Discriminant |
Eigenvalues |
0 3+ -2 1 11+ 13+ 4 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,1,-8609,307394] |
[a1,a2,a3,a4,a6] |
Generators |
[-64:769:1] [4:522:1] |
Generators of the group modulo torsion |
j |
53021770514432/585024687 |
j-invariant |
L |
7.616823807649 |
L(r)(E,1)/r! |
Ω |
0.90034990588323 |
Real period |
R |
0.70498737562143 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000228 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
89661b1 |
Quadratic twists by: -11 |